update in basic_2

[helm.git] / matita / matita / contribs / lambdadelta / basic_2 / rt_computation / csx_cpxs.ma

diff --git a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
index baba7a13128c28adadd4d7e6ed848e26af54f665..6995ad65686a19b12f1f3e23bca449d390840b42 100644 (file)
--- a/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
+++ b/matita/matita/contribs/lambdadelta/basic_2/rt_computation/csx_cpxs.ma
@@ -36,27 +36,23 @@ qed-.
 
 (* Eliminators with extended context-sensitive rt-computation for terms *****)
 
-lemma csx_ind_cpxs_teqx (G) (L):
+fact csx_ind_cpxs_aux (G) (L):
       ∀Q:predicate term.
       (∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
         (∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → (T1 ≛ T2 → ⊥) → Q T2) → Q T1
       ) →
       ∀T1. ❪G,L❫ ⊢ ⬈*𝐒 T1 →
-      ∀T0. ❪G,L❫ ⊢ T1 ⬈* T0 → ∀T2. T0 ≛ T2 → Q T2.
+      ∀T2. ❪G,L❫ ⊢ T1 ⬈* T2 → Q T2.
 #G #L #Q #IH #T1 #H @(csx_ind … H) -T1
-#T1 #HT1 #IH1 #T0 #HT10 #T2 #HT02
-@IH -IH /3 width=3 by csx_cpxs_trans, csx_teqx_trans/ -HT1 #V2 #HTV2 #HnTV2
-lapply (teqx_tneqx_trans … HT02 … HnTV2) -HnTV2 #H
-elim (teqx_cpxs_trans … HT02 … HTV2) -T2 #V0 #HTV0 #HV02
-lapply (tneqx_teqx_canc_dx … H … HV02) -H #HnTV0
-elim (teqx_dec T1 T0) #H
-[ lapply (teqx_tneqx_trans … H … HnTV0) -H -HnTV0 #Hn10
-  lapply (cpxs_trans … HT10 … HTV0) -T0 #H10
-  elim (cpxs_tneqx_fwd_step_sn … H10 …  Hn10) -H10 -Hn10
-  /3 width=8 by teqx_trans/
-| elim (cpxs_tneqx_fwd_step_sn … HT10 … H) -HT10 -H #T #V #HT1 #HnT1 #HTV #HVT0
-  elim (teqx_cpxs_trans … HVT0 … HTV0) -T0
-  /3 width=8 by cpxs_trans, teqx_trans/
+#T1 #HT1 #IH1 #T2 #HT12
+@IH -IH /2 width=3 by csx_cpxs_trans/ -HT1 #V2 #HTV2 #HnTV2
+elim (teqx_dec T1 T2) #H
+[ lapply (teqx_tneqx_trans … H … HnTV2) -H -HnTV2 #Hn12
+  lapply (cpxs_trans … HT12 … HTV2) -T2 #H12
+  elim (cpxs_tneqx_fwd_step_sn … H12 …  Hn12) -H12 -Hn12
+  /3 width=4 by/
+| elim (cpxs_tneqx_fwd_step_sn … HT12 … H) -HT12 -H
+  /3 width=6 by cpxs_trans/
 ]
 qed-.
 
@@ -67,5 +63,5 @@ lemma csx_ind_cpxs (G) (L) (Q:predicate …):
       ) →
       ∀T. ❪G,L❫ ⊢ ⬈*𝐒 T → Q T.
 #G #L #Q #IH #T #HT
-@(csx_ind_cpxs_teqx … IH … HT) -IH -HT // (**) (* full auto fails *)
+@(csx_ind_cpxs_aux … IH … HT) -IH -HT // (**) (* full auto fails *)
 qed-.